The government has refused to deny that Rupert Murdoch asked Theresa May to reappoint Michael Gove to the cabinet or face a bad press in his newspaper titles, insisting that cabinet roles are selected on “merit and experience”.

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In the government’s response, Damian Green, the first secretary of state, did not address Watson’s questions about Murdoch directly but said that decisions about cabinet and ministerial roles were taken by the prime minister alone.

Green said in a letter: “All those appointed by Her Majesty the Queen to cabinet and ministerial roles are selected by the prime minister based on their merit and experience, drawing on each member’s best talent. The decision is the prime minister’s alone. Your email raised the important issue of transparency about meetings with senior media executives.

“Government ministers are fully transparent about such meetings, but I observe that the Labour party has still failed to publish any information about shadow cabinet members’ meetings with senior media executives since Jeremy Corbyn became leader – including your own meetings.”

Labour insiders insist the delay in publishing details of meetings with media executives is due to an administrative issue and that it will be resolved soon.

Watson said people would draw their own conclusions about the lack of a denial regarding Murdoch asking for Gove to be reappointed. The deputy Labour leader said he enquired about Murdoch’s influence because it had been suggested to him that the media mogul asked for Gove to return to the cabinet.

“I asked Theresa May to deny a deeply worrying allegation that had been made to me about her and she refused to do so,” Watson said. “It’s such an easy thing to deny - unless it’s true. People will draw their own conclusions.

“With 21st Century Fox’s bid for Sky being considered by the government right now, questions about Rupert Murdoch’s influence over Theresa May were already being asked. This makes them all the more relevant.”

Following his departure from the cabinet, Gove was hired as a columnist by the Times, which is owned by Murdoch’s News Corp, on a reported £150,000 a year. Gove then became embroiled in a row earlier this year when it was reported that Murdoch was in the room when he interviewed the new US president, Donald Trump.

Karen Bradley, the culture secretary, is in the process of deciding whether to refer to the Competition and Markets Authority a £11.7bn bid from 21st Century Fox for the 61% of Sky that it does not own. Fox is controlled by Rupert Murdoch and his sons Lachlan and James.

Bradley has said she is “minded” to refer the deal to the CMA due to concerns about media plurality raised by Ofcom, the media regulator, in a report about the proposed takeover.

A consultation about the deal closed on Friday. Bradley’s Department for Digital, Culture, Media and Sport (DCMS) is now considering the submissions before announcing a final decision.

Fox’s lawyers, Allen & Overy, said in a letter to DCMS that it was “confident” a decision could be made in the “coming days”.

However, Allen & Overy said in its letter: “21CF [21st Century Fox] trusts that the secretary of state will dismiss these flagrant political attempts to interfere in the regulatory process and its timing, which are in stark contrast to the respect for the independence of Ofcom that the authors of the letter had until recently promulgated.

“By doing so, 21CF is confident that the secretary of state should be able to reach a final decision on a reference to the CMA in the coming days, thereby avoiding any further delay to the timetable for concluding the regulatory review of the proposed transaction.”

In response to the letter, Miliband said: “Clearly the Murdochs are rattled by the rightful scrutiny their bid and their corporate record are receiving. The secretary of state must not bow to the outrageous attempts to intimidate her by the Murdochs.”